International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
A COMBAT MODEL ADAPTABLEFOR
EVALUATING THE IMPLEMENTABILITY
OF PROJECTS AND PROGRAMMES
Navy Captain MO Oladejo
Department of Mathematics, NDA, Kaduna
ABSTRACT
Complexity of military combat modeling is being highlighted by a review using Lanchester equations in order to determine
damage/coverage of weapon. This in turn was used as a measure of capability/implementability. Some concepts in reliability
have been adopted and applied to a class of problems found in a system whose component items have chain link. The
proportion of available logistics items needed to execute projects/programmeswas used,in recent application concept, to obtain
the Availability Capability (AC) via reliability, and the Implementability or Delivery Capability (Damage Coverage) (DC) via
mean Time To Failure (MTTF). A military formation, DC was found to be 30.9, which yielded Percentage implementability.
Keywords:- Projects, Reliability, Mean Time to Failure, Implementability, Availability, Delivery, Damage, Capability,
Coverage, Logistics.
1.INTRODUCTION
The modeling and analysis of military combat using differential equations (DE) were rigorously, and exhaustively
handled by Taylor (1973), (1974) and (1975). Some of the results obtained are being given below.
1. Lanchester Fundamental Duel (One-on-One)
Deterministic Linear (Ancient) Law DE:
=-r ,
= b ; is the Blue strength or forcelevel.
= - b,
= r, is the Red strength or force level.
=-r ,
= b ; is the Blue strength or force level.
= - b,
= r, is the Red strength or force level.
Where b is number of Blue units remaining at time t ( at t = 0, b = B) r = is number of Red units remaining at time t
( at t = 0, r = R)  is the rate at which single Blue unit Kills Red units. is the rate at which single Red unit kills Blue
units. The time independent solution of this system, Taylor (Taylor J, 1974) is given by ( B2 – b2) =  (R2 – r2) If is
the Blue attrition rate of single round (bullet), and
is rate of fire of each weapon then the overall Blue attrition rate 
=
, and similarly for Red  =
Using the Principle of War based on (encourages) “Rapid Fire or High
Attrition” the optional solutions, Taylor [13] are given by
a.
Blue Force wires
b.
Red Force wires
c.
Parity (No Victor No Vanquished).
The time dependent solutions are:
a. b = B cosh
b. r = r cosh
2. Lanchester Indirect Fire (Combinatories)
Deterministic Square (Modern) Warfare Law DE:
=-
=
is Blue Kill rate
=-
,=
is Red Kill rate
Where Ar, Ab = areas where Red and Blue forces are located respectively.
Aer ,Aeb = areas of effectiveness of a single shot from Red and Blue respectively.
fr, fb = rates of fire of Red and Blue weapons respectively.
Volume 3, Issue 11, November 2014
Page 10
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
The notion of square is derived from the dependence on the squares of the quantities (ORBAT/Logistics) or distribution
of fire over the areas. The solution obtained by this square law is based on the Principle of War “Concentration of
Force”. The time independent solution of this system, Taylor (1974) is given by
Kb (B – b) = Kr (R – r) At the
instance of supporting fire units, e.g. Artillery , the DE describing the engagements are:
= - (1 - )
= -
- r
- r
= - (1 - )
= -
- b1
- b1
= no of Blue, Red Infantry units remaining at time t,
= no of Blue, Red Artillery units remaining at time t,
Kxy
= Kill rate of side with x units when engaging the opposing force of y units.
The solutions to these non deterministic square law DE, are numerous due to the range of , and various combinations
of attrition rates and force levels of contending forces. This research looked at combat modeling devoid of DE
approach, which has been exhaustively dealt with by JG Taylor. Output evaluations are numerous and varied depending
on the target, Taylor (1973), Taylor (1974)b just like comparison of availability of brakelights, Asalor (1984),
manpower planning, Bartholomew (1991), forecasting applications Da lurgio (1988), applications in probability, Feller
(1957), industrial engineering applications, Haribaskaran (2005). Feasibility studies have been conducted to determine
viability of projects and programmes, Theoretical Development, Oladejo and Ovuworie, (2006), Theoretical
Development, Oladejo (1995), Theoretical Development and Application, Oladejo, (2008). The success or
implementability of programmes and projects are being tackled using some models that have not included percentages
or proportions as inputs, as is the case in the reliability model that uses hazard/failure rates, to get output as delivery
capability based on the proportions of available logistics. Proportions are here being considered and used instead of
reliability, reliability and life testing, Barlor and Proschan, (1975), control and simulation, Edward and Lees, |(1973).
The proportion of each item is taken as its reliability. The overall reliability of the system is obtained and is called
Availability Capability (AC). In this work, the computed MTTF are called and used as the Implementability of
project/programmes, reliability and life testing Barlor and Proschan, (1975), energy projection, Gregoria, (1979),
reliability testing, Oroge (1991). This recent application concept has been extended to determine the Delivery
Capability (DC) which was used to obtain Implementability. In the illustrative example using military formation, the
DC was used as the evaluated Damage Capability (DC) of the formation weapon system. This damage capability was
calculated and used to determine the Implementability of the task/project.
2.METHODOLOGY
Using reliability theory and Spectral analysis models were derived for forecasting damage coverage (delivery capability)
and hence determine implementability of chosen project. Number Cruncher Statistical (NCS) package was used to
obtain Fourier Analysis Model using derived coefficients an and bn that are significant. Thereafter, used these models
to forecast output, damage coverage, and ultimately the implementability of project/programs. For every component
item calculate the proportion p, and the percentage of the items available, then compute the various Availability
Capability (AC) and then the Fourier Analysis and Regression models would be derived for forecasting target hit and
damage outcomes. The result obtained would be used to determine the delivery capability/Implementability.
Availability Capacity
Series system:
AC =
=
,
where t, time to failure is exponentially distributed.
Parallel system:
AC
=
=
components have same reliability
= 1- [1 – e-t]n, constant failure rates
Volume 3, Issue 11, November 2014
Page 11
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
Delivery Capability
Series system: DC
where ao = 2 mean value of f() (Observed values)
an = 2 mean value of f() Cos n
bn = 2 mean value of f() Sin n
the computed values are on Table 2. Let Probability Density Function (Pdf) of Soldiers/riffles for the Ex be SRS i.e.
Discrete Uniform. The mapping involved is bijective, since the correspondences between the sets of soldiers/Riffle  F
are injective and surjective. Then the PDF of Fourier forecast values is also discrete uniform.
Definition: The Damage Coverage  Capability  Implementability I = F/n, is the corresponding value obtained by
calculating the discrete uniform pdf of the Fourier predicted value. The value obtained should be x 100% to get the %
of forecast observation implementable.
Applications
1. Shooting Range Exercise
Table 1 gives the target hit recorded in Exercise Marksmanship (a soldier fires shots from a riffle at a stationary
calibrated target) and the calculated damages with their corresponding Fourier series values that can be used to
forecast.
Table 1. Coefficient of Derived Model of Soldier/weapon range classification (Single Firer)
SN Sld/Riffle
Tgthit r
R
w
Iw
Dw
F1 I
Ip
0
s X
1
NDA1/R1
15
0.50
0.615
0.3075
4.61250
12
3.622649
2
NDA2/R2
4
0.133
0.160
0.02128 0.08512
24
0.066853
3
NDA3/R3
20
0.667
0.699
0.44622 8.92446
36
7.009254
4
13
0.433
0.099
0.04287 0.55727
48
0.437679
5
9
0.300
0.942
0.2826
2.5434
60
1.997582
6
11
0.367
0.827
0.30351 3.33860
72
2.62213
7
23
0.767
0.625
0.47938 11.025625
84
8.659506
8
19
0.633
0.396
0.25067 4.76269
96
3.740608
9
6
0.200
0.118
0.0236
0.1416
108
0.111212
10
NN01/R11
5
0.167
0.064
0.0107
0.0534
120
0.04194
11
NN02/R12
27
0.900
0.756
0.6804
18.3708
132
14.42839
12
8
0.267
0.394
0.1052
0.8416
144
0.660991
13
25
0.833
0.066
0.0550
1.3745
156
1.07953
14
16
0.533
0.214
0.1141
1.8250
168
1.433352
15
10
0.333
0.922
0.3070
3.0703
180
2.411408
16
NN01/R21
14
0.467
0.206
0.0962
1.3468
192
1.057774
17
17
12
0.400
0.749
0.2996
3.5952
204
2.823663
18
18
22
0.733
0.228
0.1672
3.6784
216
2.889009
19
19
19
0.633
0.261
0.1652
3.1391
226
2.465443
20
NN10/R20
3
0.1000
0.025
0.0025
0.0075
240
0.00589
21
NAF011/R21 6
0.2000
0.968
0.1930
1.1580
252
0.909491
22
NAF02/R22
7
0.233
0.265
0.0618
0.4328
264
0.33992
23
23
26
0.8670
0.096
0.0832
2.1648
276
1.70023
24
24
15
0.5000
0.267
0.1335
2.0025
288
1.57276
25
19
0.6330
0.154
0.0975
1.8522
300
1.454714
Volume 3, Issue 11, November 2014
Page 12
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
26
27
28
29
30
NAF10/R30
NDAn/Rn
9
21
17
12
30
0.3000
0.7000
0.5667
0.4000
0.999
0.557
0.027
0.287
0.610
0.033
0.1671
0.0189
0.1626
0.244
0.0330
1.5039
0.3969
2.7649
2.9280
0.9890
312
324
336
348
360
ISSN 2319 - 4847
1.18116
0.311725
2.171547
2.299646
0.776759
Graph 1: Degrees against Dw (Example 1)
F1 = F(, Dw) = Y’ is forecasts obtained after deriving appropriate model (see Table 3).The choice of spectral analysis
to derive the model for this research was predicated on the sinusoidal outputs, as depicted on graphs of original data.
No of hits = x  damage to tgtsor no of successful hit. R  reliability of weapon (riffile) or accuracy of weapon.
raccuracy of Sld (wpn handler) =
=
, n = no of round (bullets) issued for firing. .
w =rR =  damage coefficient
Iw = wx = = rRx = = impact on tgt
Dw = IwP(A) is damage to tgt, P(A) is proportion of tgt covered by bullets
i = (12i)o =
, i = 1,2,3,…,30 (angles require in deriving Fourier Model)
I  implementability = F1/n
I convert SN & Soldier/Riffle to angular values i.e
Dw translates to proportion of task (project/Programme) assigned that can be achieved.
= Iw
Fig 2: Single Firer target
Result
rb = 0.1m , Ab = 0.01  m2, p(Ab) =

ri = 0.5m , Ai = 0.25  m2, p(Ai) =

r0 = 1.0m ,Ab = 0.01  m2, p(Ab) =

Prob of a pt in any circular target or of radius r tc is given by P(Atc) =
Volume 3, Issue 11, November 2014
Page 13
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
I(k) =
T=
ISSN 2319 - 4847
+ SS, (sum of squares) k = 1,2,……,
≥ 0.5, test statistics for significance of coefficients to be accepted in the
equation/model.
RSEk =
for a season.
Table 2 : Fourier Analysis of Single Firer
Frequenc
y
Wavelengt
h
Period
Cosine(a's
)
Sine(b's)
0.307178
20.45455
15.20152
-1.958461
-1.591235
0.4049164
15.51724
2.104604
-0.8883041
-0.304122
0.5026549
12.5
12.30483
-1.828336
-1.345892
0.6003932
10.46512
8.176512
-0.2259184
-1.836826
0.6981317
9
2.945911
-4.26E-02
-1.110029
0.7958701
7.894737
4.706373
0.2155723
-1.387418
0.8936086
7.03125
5.07279
1.153949
0.991347
6.338028
0.8317432
1.089085
5.769231
1.895862
0.155545
9
-0.890667
0.319906
1
1.186824
5.294117
2.793575
1.008405
-7.97E-02
0.391522
5
1.284562
4.891304
5.023153
0.1769834
1.439712
1.382301
4.545455
8.080674
-1.068588
1.497647
1.480039
4.245283
14.59759
-2.46174
-0.23337
1.577778
3.982301
9.859504
1.95E-02
1.675516
3.75
3.254531
0.8742769
1.773255
3.543307
4.16041
-1.268177
-2.032131
0.773882
9
0.366655
6
1.870993
3.358209
1.485811
-0.5866731
-0.527437
1.968731
3.191489
-0.4590535
-0.632974
2.06647
3.04054
1.459578
0.306285
6
0.2882544
-0.212617
2.164208
2.903226
2.214139
-0.9629127
1.60E-02
45.85969
30.974533
9
10.224411
3
13.070319
2
4.6678125
7
4.5853993
5
0.9622244
1
6.9559224
5
2.261947
2.777778
6.337994
8.43E-02
-1.62719
19.911406
2.359685
2.662722
4.295391
1.338243
2.457424
2.556818
1.570526
0.3266777
9.14E-02
0.742389
5
2.555162
2.459016
3.513019
-0.2167711
2.6529
2.368421
6.388424
-1.61436
1.193541
0.264232
9
2.750639
2.284264
-0.5014824
-0.956081
2.848377
2.205882
2.782605
0.510613
6
13.494368
4.9339536
7
11.036473
7
20.069829
3
8.7418117
7
-6.81E-02
-0.457431
1.6041399
0.2424829
Volume 3, Issue 11, November 2014
I
47.756987
4
6.6118068
3
38.656783
5
25.687266
6
9.2548566
9
14.785500
9
15.936639
7
5.9560249
8
0.4886620
4
8.7762788
4
15.780703
3
25.386201
4
RSE
Spectrum
T
2.98481171
0.41323792
7
2.41604897
1
1.60545416
1
0.57842854
3
0.92409380
8
0.99603997
8
0.37225156
1
0.03054137
7
0.54851742
8
0.98629395
3
1.58663758
6
2.86623062
7
1.93590836
8
0.63902570
7
0.81689495
3
0.29173828
6
8.65306
-1.52406
7.204719
-0.4652
10.24067
-1.32145
5.561211
-7.10635
3.826142
-13.5716
4.889582
4.2867
3.484326
0.863158
1.025704
0.447556
1.47456
0.125953
3.908364
0.543946
6.551914
5.572805
11.33913
-1.4848
12.22855
-1.16431
6.557017
99.12105
3.707471
0.730919
2.82311
-0.64415
1.472694
0.882931
8
-0.49728
1.260212
0.208632
4.276066
-0.45149
5.316692
14.76196
2.932959
0.630228
2.541772
0.943964
4.950722
-3.18206
4.585515
-0.777
1.646609
-1.0895
1.053444
-1.47156
0.28658746
0.06013902
6
0.43474515
3
1.24446287
3
0.84339800
2
0.30837210
4
0.68977960
7
1.25436432
9
0.54636323
6
0.10025874
4
-0.6243
Page 14
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
2.946116
2.132701
1.596275
0.6815157
-0.451866
3.043854
2.06422
4.760706
0.2481965
1.390165
5.0148462
7
14.956201
7
3.141593
2
7.925162
-1.822
9.68E-14
24.89763
0.31342789
2
0.93476260
8
1.55610187
5
ISSN 2319 - 4847
3.178491
0.459898
6.342934
3.76622
6.342934
-0.85406
Table 3 : Forecasts by Derived Spectral Model ( = 120)
Y=X
Y'
I
11
1.404065
5.395664
23
-0.82755
-3.18018
5
-0.10182
-0.39128
27
0.980009
3.766064
16
1.466358
5.635049
10
-1.14322
-4.39327
6
-0.83558
-3.21104
7
0.522388
2.007478
26
0.190881
0.733534
12
-1.39531
-5.36202
Test of
Significance as coefficients of model which lead to acceptance or otherwise. The spectral analysis
model of example 1, a single firer, is given by this formula Y’ =
+
cos n
Because the Fourier Analysis Model does not give accurate forecasts other models must be found for the same exercise.
The models considered were:
a. Linear, Y11= -0.957 + 0.199X
b. Logarithnmic, Y1g = - 3.72 + 2.390 In(X)
c. Y1q = -0.959 + 0.258X – 0.002X2
TABLE 4 : Regression Forecasts (Using the formulae)
15
16
17
18
19
20
21
10
14
12
22
19
3
6
Volume 3, Issue 11, November 2014
1.033
1.829
1.431
3.421
2.824
-0.36
0.237
1.783178
2.587347
2.218927
3.667591
3.317209
-1.09432
0.562305
1.421
2.261
1.849
3.749
3.221
-0.203
0.517
Page 15
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
S/N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
X
15
4
2
13
9
11
23
19
6
5
27
8
25
16
10
14
12
22
19
3
6
YIL
2.028
-0.161
3.023
1.63
0.834
1.232
3.62
2.824
0.237
0.038
4.416
0.635
4.018
2.227
1.033
1.829
1.431
3.421
2.824
-0.36
0.237
Yig
2.75224
-0.40676
3.4398
2.410229
1.531367
2.01097
3.773831
3.317209
0.562305
0.126557
4.15705
1.249865
3.973113
2.906487
1.783178
2.587347
2.218927
3.667591
3.317209
-1.09432
0.562305
Yiq
2.461
0.041
3.401
2.057
1.201
1.637
3.917
3.221
0.517
0.281
4.549
0.977
4.241
2.657
1.421
2.261
1.849
3.749
3.221
-0.203
0.517
22
23
24
25
26
27
28
29
30
7
26
15
19
9
21
17
12
30
0.436
4.217
2.028
2.824
0.834
3.222
2.426
1.431
5.013
0.930725
4.066851
2.75224
3.317209
1.531367
3.556409
3.05138
2.218927
4.408862
0.749
4.397
2.461
3.221
1.201
3.577
2.849
1.849
4.981
2. Brigadier EZA, Military Formation
Table 5 gives the ORBAT of a military formation (Brigade EZA).
Network Pi(t=1)
ℷii
Pi(2)
ℷ2i
Pi(3)
A
0.55
0.59784
0.55
0.29892 0.55
B,C
0.9, 0.6
0.10536
0.9,0.6
0.05268 0.9,0.6
0.51083
0.25542
(D,E,F)
(G,H)
(0.7,0.8,0.5)
, (0.4,0.7)
0.35668
(0.7,0.8,0.5) 0.17834 (0.7,0.8,0.5
0.22314
,
0.11157 )
0.69315
(0.4,0.7)
0.34658 (0.4,0.7)
0.091629
0.45815
0.35668
0.17834
I
0.3
1.20397
0.3
0.60199 0.3
Logistics Items in this military formation
A  Arsernal/Armoury D  Bayonetted Riffle B  Ammo
C  Shell
E  RPG
F  GPMG
G  Rocket Luncher
H  Artillery/Bofors
I  Damage coverage calculation/evaluation
ISSN 2319 - 4847
ℷ3i
0.19928
0.03512
0.17028
0.11889
0.07438
0.23105
0.30543
0.11889
0.40132
Fig 4 System network
Volume 3, Issue 11, November 2014
Page 16
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
Implementability optimal value is the overall or cummulative delivery capability implementable by the network given
above.
Computations using methodology were conducted for the various AC and DC. The values of p(1),ℷ1 ,p(2),ℷ2 ,p(3),ℷ3 ,
from the table above were used in the analysis.
3.RESULT
Availability Capacity for p(1),ℷ1 :
A : AC1 = 0.55, pi(t) is proportion available at time t
BC: AC2 = 1 – (1 – 0.9)(1 – 0.6) = 0.96
DEF: AC3 = 1 – (1 – 0.7)(1 – 0.8)(1 – 0.5) = 0.97
G,H: AC4 = 1 – (1 – 0.4)(1 – 0.7) = 0.72
(D,E,F),(G,H): AC5 = 1 – (1 – 0.97)(1 – 0.72) = 0.9916
I: AC6= 0.3
AC5 = AC1.AC2.AC5.AC6 = 0.15707  15.71% , expendable available logistics.
Delivery Capability for p(1),ℷ1 :
A: MTTFA = MTTF1
=
= 1.67269, since I = -Inpit-1 is the supply/replenishment rates.
BC :MTTFB,c = MTTF2
= 9.49127 + 1.95760 – (1.62288)
= 9.82599 DEF :MTTFD,E,F
= 7.68847 – (1.72467 + 1.09136)
+ 0.78557 = 5.65801
GH :MTTFG,H1.09136 + 2.80363 – (0.78557) = 3.10942
DEF,GH : MTTFD,E,F,G,H = MTTF3= 18.12579 + 3.05979 – (2.61787) = 18.56771,where DEF = DEF
= 0.05517,andGH = GH = 0.32682
I :MTTI = MTTF4=
= 0.83059
MTTFs =
= 30.89698
This DC is the Damage Capability of the Military Formation.
Availability Capacity for p(2),ℷ2 :
A : AC1 = 0.55, pi(t) is proportion available at time t
BC: AC2 = 1 – (1 – 0.9)(1 – 0.6) = 0.96
DEF: AC3 = 1 – (1 – 0.7)(1 – 0.8)(1 – 0.5) = 0.97
G,H: AC4 = 1 – (1 – 0.4)(1 – 0.7) = 0.72
(D,E,F),(G,H): AC5 = 1 – (1 – 0.97)(1 – 0.72) = 0.9916
I : AC6 = 0.3 AC5 = AC1.AC2.AC5.AC6 = 0.15707  15.71% , expendable available logistics.
Delivery Capability for p(2),ℷ2:
A: MTTFA = MTTF1
=
= 3.34538, since I = -Inpit-1 is the supply/replenishment rates.
BC :MTTFB,c = MTTF2=
= 18.98254 + 3.91512 – (3.24570)
= 19.65196 DEF : MTTFD,E,F
= 14.57025 – 5.63204 + 1.57112 = 10.50933
GH : MTTFG,H= 2.18269 5.60727 – 1.57112 = 6.21884
DEF,GH : MTTFD,E,F,G,H = MTTF3 = 10.50933 + 6.21884 = 16.72817,where DEF = DEF = 0.0069,and GH = GH =
0.08171
I : MTTI = MTTF4 = = 1.66116
MTTFs =
= 41.38667
This DC is the Damage Capability of the Military Formation.
Availability Capacity for p(3),ℷ3 :
A : AC1 = 5.01811, pi(t) is proportion available at time t
BC: AC2 = 28.47380 + 5.87268 – (4.86855) = 34.34648 – 4.86855 = 29.47793
DEF: AC3 = 26.18405 – 8.44840 + 2.35682 = 20.09247
G,H: AC4 = 3.27407 + 8.41114 – 2.35671 = 9.3285
(D,E,F),(G,H): AC5 = 20.09247 + 9.3285 = 29.42097
DEF = DEF = 0.0020,andGH = GH = 0.03631
I : AC6 = 2.49178
Volume 3, Issue 11, November 2014
Page 17
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
AC5 = AC1.AC2.AC5.AC6 = 0.15707  15.71% , expendable available logistics.
Delivery Capability for p(3),ℷ3:
A: MTTFA = MTTF1=
=
= 5.01811, since I = -Inpit-1 is the supply/replenishment rates.
BC :MTTFB,c = MTTF2=
– (4.86855) = 34.34648 – 4.86855 = 29.47799
= 28.47380 + 5.87268
DEF : MTTFD,E,F
=26.18405–(8.44840) + 2.35682=
20.09247
GH : MTTFG,H=3.27407 + 8.4114 – (2.35671) = 9.3285
DEF,GH : MTTFD,E,F,G,H = MTTF3 = 20.09247 + 9.3285 = 29.42097 ,where DEF = DEF = 0.00204,and GH = GH
= 0.03631
I : MTTI = MTTF4 =
= 2.49178
MTTFs =
= 71.4269
This DC is the Damage Capability of the Military Formation.
Table 6: Spectral Coefficients
yt

f() = Dw
f() Cos
f()Sin
120
24.276
y0
-12.138
21.024
240
32.518
y1
-16.259
-28.161
360
56.121
y2
56.121
0
total
112.915
27.724
-7.137
f() Cos2
-12.138
-16.259
56.121
27.724
f()Sin2
21.024
-28.161
0
-7.137
F2 (240, 32.518) = 56.794
F2 (360, 56.121) = 112.240
F2 (0, 0) = 112.24
Forecast
F2 (480, 0) = 48.553
These Computed Values were used to obtain Coefficient of Model
Table 7 Spectral Model Goodness of Fit
DC = Iw
Dw - F2
Yp(Goodness Fit From Computer Model)

F(:D
w) = F2
D =I
w
0
120
240
360
480
i
1
2
3
30.897
41.387
71.427
-
h
1
2
3
w
24.276
32.518
56.121
112.915
p(i)
P(1)
P(2)
P(3)
112.240
48.553
56.794
112.240
48.553
217.587
Dw
24.276
32.518
56.121
112.915
24.277
24.276
56.119
Table 8 =DwVs I
F2

120
48.553
240
56.794
360
112.24
217.587
Very Poor
Very Poor
Very Poor
fh
1/3
1/3
1/3
ei
24.277
24.276
56.119
104.672
=34.891
I
0.2231
0.2610
0.5158
Ip
0.2231
0.2610
0.5158
Table 7 and 8 show that the Spectral derived model is not suitable for forecasting data on these tables. The values of I
also corroborate undependability of this model for forecasting because the values x 100% shows the level
implementable which are very low. The unsuitability of Fourier model warranted derivation of alternative model. The
derived alternative regression models are given below:
Volume 3, Issue 11, November 2014
Page 18
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
Table 9: Value to obtain Regression Coefficient
Table 10 : Forecast of Quadratic Model
Fig 12: Degrees vs Dw (Example 2)
Volume 3, Issue 11, November 2014
Page 19
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 11, November 2014
ISSN 2319 - 4847
4.DISCUSSION
In the case of a single firer (example 1), a spectral model was derived whose pattern (graph) appears sinusoidal but
does not yield acceptable results. Even the implementability values are low and fluctuate stochastically. The AC are the
same for the three stages, because the respective AC at different stages are fixed, due to the assumed p(available
proportion that now stands as reliability). Whereas the DC varied according to the values of t, the stages of the system.
It was observed that as the stages increased decreased while the DC increased. This means that on the long run the
DC (damage capability) also increased even at lower rates of logistics supply. This is so because for all values of p>0,
however infinitesimal, a certain amount of damage would be recorded.
5.CONCLUSION
The results of damages to target by single firer and weapons system combat, were used to obtain implementability of
individual (dual) and group (indirect fire or weapons system) projects/programmes or tasks, with the aid of appropriate
pdf transformations. These derived models were used to determine the implementability as shown on Tables 1 and 8.
6.FURTHER RESEARCH
Further research can be carried out using various values of x,r,R, ,n p and  to determine Dw, FAC and DC of systems.
REFERENCE
[1] Asalor, J.O. (1984) Comparison of availability of brakelights of Platform Vehicles on some roads in Nigeria and
Italy, Nigeria Engineer vol. 19, No 3 and 4.
[2] Barlor, R.E. and Proschan, F. (1975): Statistical Theory of Reliability and Life Testing – HRW Inc. NY.
[3] Bartholomew, J., Forbes, A.F. and McCleans (1991): Statistical Techniques for Manpower Planning, John
Wiley & Sons, NY.
[4] De Lurgia, S.A. (1998): Forecasting Principles and Applications Irwin/McGraw – Hill Co.
[5] Edward, E. Lees, F.P. (1973): “Man – Machine System Reliability”, Man and Computer in Process Control.
[6] Feller, W. (1957): An Introduction to Probability Theory and Its Application 3rd Edition, John Wiley &
Sons, Inc., Vol. 1 and 2.
[7] Grigoria, M. (1979) “Reliability of Active Parallel System”, Journal of the Energy Division.
[8] Haribaskaran, G. (2005): Probability, Queuing Theory and Reliability Engineering, LAXMI
PUBLICATIONS (P) Ltd, New Delhi, India.
[9] Oladejo, M.O., Ovuworie, G.C. (2006): Adequacy of C3I Models for Training, NJISS, Vol. 6, No. 4, Oct.
[10] Oladejo, M.O. (2008): Redundancy Considerations In The Minimization of Manpower Wastages In The
Nigerian Navy General List, AJDS, Vol. 15.
[11] Oladejo, M.O. (1995): Some Development in Military Operations Analysis: Readiness, C3I, and Training,
PhD Thesis, Production Engineering Department, University of Benin.
[12] Oroge, C.O. (1991): Fundamentals of Reliability and Testing Methods (First Edition), Soji Press Ltd, Kaduna.
[13] Taylor J. ”Target Selection in Lanchester Combat: Linear-Law Attrition Process” Naval Rea. Log. Quart.
20,673697. (1973).
[14] Taylor, “Lanchester-type Model of Warfare and Optional Control”, Naval Res, Log.Quart 21, 79-106 (1974).
[15] Taylor, “Target Selection in Lanchester Combat: Heterogeneous Forces and Time-Dependent AttritionRate Coefficients,“ Naval Res.Log. Quart. 21 683-704 (1974).
Volume 3, Issue 11, November 2014
Page 20